Mt/G/∞ queues with sinusoidal arrival rates
Management Science
The physics of the Mt/G/ ∞ symbol Queue
Operations Research
A heavy-traffic analysis of a closed queueing system with a GI/\infty service center
Queueing Systems: Theory and Applications
Peakedness Measures for Traffic Characterization in High-Speed Networks
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
The Pht/Pht/8 Queueing System: Part I--The Single Node
INFORMS Journal on Computing
A Diffusion Approximation for the G/GI/n/m Queue
Operations Research
Staffing of Time-Varying Queues to Achieve Time-Stable Performance
Management Science
Two-parameter heavy-traffic limits for infinite-server queues
Queueing Systems: Theory and Applications
Infinite-server queues with batch arrivals and dependent service times
Probability in the Engineering and Informational Sciences
Two-parameter heavy-traffic limits for infinite-server queues with dependent service times
Queueing Systems: Theory and Applications
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This paper investigates the impact of dependence among successive service times on the transient and steady-state performance of a large-scale service system. This is done by studying an infinite-server queueing model with time-varying arrival rate, exploiting a recently established heavy-traffic limit, allowing dependence among the service times. This limit shows that the number of customers in the system at any time is approximately Gaussian, where the time-varying mean is unaffected by the dependence, but the time-varying variance is affected by the dependence. As a consequence, required staffing to meet customary quality-of-service targets in a large-scale service system with finitely many servers based on a normal approximation is primarily affected by dependence among the service times through this time-varying variance. This paper develops formulas and algorithms to quantify the impact of the dependence among the service times on that variance. The approximation applies directly to infinite-server models but also indirectly to associated finite-server models, exploiting approximations based on the peakedness (the ratio of the variance to the mean in the infinite-server model). Comparisons with simulations confirm that the approximations can be useful to assess the impact of the dependence.